SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\FreeLie"];
<< FreeLie.m

bmor=LieMorphism[{⟨"x"⟩->LieSeries[⟨"y"⟩],⟨"y"⟩->LieSeries[⟨"z"⟩]}]

BCH[7]//Last

bmor[BCH[7]//Last]

bmor[⟨"xxxxxxy"⟩]

bmor[Cases[BCH[7]//Last, _LW, Infinity]]

Total[Take[bmor[Cases[BCH[7]//Last, _LW, Infinity]],15]]